_Antti Karttunen _, Oct 28 2001

<a href="/Sindx_index/Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

<a href="/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

nonn,new

nonn

When an infinite planar binary tree is mapped breadth-first-wise from left to right (1 is at top, 2 is its left, and 3 its right child, 4 is 2's left child, etc.) then this permutation induces such rearrangement of its nodes, that on the right side every node replaces its right child, on the left side the left children replace their parents, and the right children are reflected to the right side, to be the left children of their new parents.

<a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

A057114, A065269, A065275, A065281, A065287. Inverse: A065264, conjugated with A059893: A065265, and the inverse of that: A065266.

nonn,new

nonn

Infinite binary tree inspired permutation of N: 1 -> 3, 11ab..yz -> 11ab..yz1, 10ab..y0 -> 10ab..y, 10ab..y1 -> 11AB..Y0 (where 1AB..Y0 is the complement of 0ab..y1).

3, 1, 7, 2, 6, 13, 15, 4, 14, 5, 12, 25, 27, 29, 31, 8, 30, 9, 28, 10, 26, 11, 24, 49, 51, 53, 55, 57, 59, 61, 63, 16, 62, 17, 60, 18, 58, 19, 56, 20, 54, 21, 52, 22, 50, 23, 48, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 32, 126, 33, 124

1,1

When an infinite planar binary tree is mapped breadth-first-wise from left to right (1 is at top, 2 is its left, and 3 its right child, 4 is 2's left child, etc.) then this permutation induces such rearrangement of its nodes, that on the right side every node replaces its right child, on the left side the left children replace their parents, and the right children are reflected to the right side, to be the left children of their new parents.

<a href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

RightChildInverted := proc(n) local k; if(1 = n) then RETURN(3); fi; k := floor_log_2(n)-1; if(3 = floor(n/(2^k))) then RETURN((2*n)+1); fi; if(0 = (n mod 2)) then RETURN(n/2); fi; RETURN(2^(k+1) + ((2^(k+2))-1) - n); end;

A057114, A065269, A065275, A065281, A065287. Inverse: A065264, conjugated with A059893: A065265, and the inverse of that: A065266.

nonn

Antti Karttunen Oct 28 2001

approved